6 October 2025 6:31:05.558 PM praxis_test(): Fortran90 version Test praxis(). BEALE_TEST The Beale function. Initial point: 1 0.10000000 2 0.10000000 Function value = 12.9910 Computed minimizer: 1 3.0000000 2 0.50000000 Function value = 0.369857E-25 BOX_TEST The Box function. Initial point: 1 0.0000000 2 10.000000 3 20.000000 Function value = 1031.15 Computed minimizer: 1 1.0000000 2 10.000000 3 1.0000000 Function value = 0.333706E-25 CHEBYQUAD_TEST The Chebyquad function. Initial point: 1 0.11111111 2 0.22222222 3 0.33333333 4 0.44444444 5 0.55555556 6 0.66666667 7 0.77777778 8 0.88888889 Function value = 0.386177E-01 Computed minimizer: 1 0.43152691E-01 2 0.19309075 3 0.26632869 4 0.50000007 5 0.49999991 6 0.73367126 7 0.80690918 8 0.95684730 Function value = 0.351687E-02 CUBE_TEST The Cube function. Initial point: 1 -1.2000000 2 -1.0000000 Function value = 57.8384 Computed minimizer: 1 1.0000000 2 1.0000000 Function value = 0.204930E-24 HELIX_TEST The Fletcher-Powell Helix function. Initial point: 1 -1.0000000 2 0.0000000 3 0.0000000 Function value = 10000.0 Computed minimizer: 1 1.0000000 2 0.11162027E-10 3 0.17715151E-10 Function value = 0.372317E-21 HILBERT_TEST The Hilbert function. Initial point: 1 1.0000000 2 1.0000000 3 1.0000000 4 1.0000000 5 1.0000000 6 1.0000000 7 1.0000000 8 1.0000000 9 1.0000000 10 1.0000000 Function value = 13.3754 Computed minimizer: 1 -0.25410432E-05 2 0.22280856E-03 3 -0.48021545E-02 4 0.44089351E-01 5 -0.21206000 6 0.58710674 7 -0.96913592 8 0.94147189 9 -0.49651094 10 0.10962278 Function value = 0.271263E-12 POWELL3D_TEST The Powell 3D function. Initial point: 1 0.0000000 2 1.0000000 3 2.0000000 Function value = 1.50000 Computed minimizer: 1 1.0000000 2 1.0000000 3 1.0000000 Function value = 0.00000 ROSENBROCK_TEST The Rosenbrock function. Initial point: 1 -1.2000000 2 1.0000000 Function value = 24.2000 Computed minimizer: 1 1.0000000 2 1.0000000 Function value = 0.446274E-23 SINGULAR_TEST The Powell Singular function. Initial point: 1 3.0000000 2 -1.0000000 3 0.0000000 4 1.0000000 Function value = 215.000 Computed minimizer: 1 0.24018592E-04 2 -0.24018592E-05 3 0.99942105E-05 4 0.99942111E-05 Function value = 0.638171E-18 TRIDIAGONAL_TEST The Tridiagonal function. Initial point: 1 0.0000000 2 0.0000000 3 0.0000000 4 0.0000000 Function value = 0.00000 Computed minimizer: 1 4.0000000 2 3.0000000 3 2.0000000 4 1.0000000 Function value = -4.00000 WATSON_TEST The Watson function. Initial point: 1 0.0000000 2 0.0000000 3 0.0000000 4 0.0000000 5 0.0000000 6 0.0000000 Function value = 30.0000 Computed minimizer: 1 -0.15725087E-01 2 1.0124349 3 -0.23299162 4 1.2604301 5 -1.5137289 6 0.99299643 Function value = 0.228767E-02 WOOD_TEST The Wood function. Initial point: 1 -3.0000000 2 -1.0000000 3 -3.0000000 4 -1.0000000 Function value = 19192.0 Computed minimizer: 1 1.0000000 2 1.0000000 3 1.0000000 4 1.0000000 Function value = 0.240850E-19 MINFIT_TEST MINFIT computes part of the SVD of a matrix A. SVD: A = U * D * V' MINFIT is given A, and returns the diagonal D and the orthogonal matrix V. The matrix A: Col 1 2 3 4 5 Row 1 2. -1. 0. 0. 0. 2 -1. 2. -1. 0. 0. 3 0. -1. 2. -1. 0. 4 0. 0. -1. 2. -1. 5 0. 0. 0. -1. 2. The vector V: Col 1 2 3 4 5 Row 1 -0.288675 0.500000 -0.577350 0.500000 -0.288675 2 0.500000 -0.500000 0.240746E-15 0.500000 -0.500000 3 -0.577350 0.190820E-15 0.577350 -0.359110E-15 -0.577350 4 0.500000 0.500000 0.607563E-16 -0.500000 -0.500000 5 -0.288675 -0.500000 -0.577350 -0.500000 -0.288675 The singular values D: 1 3.7320508 2 3.0000000 3 2.0000000 4 1.0000000 5 0.26794919 Because A is positive definite symmetric, we can reconstruct it as A = V * D * V' The product A2 = V * D * V' Col 1 2 3 4 5 Row 1 2.00000 -1.00000 -0.492661E-15 -0.943690E-15 -0.163064E-15 2 -1.00000 2.00000 -1.00000 0. -0.735523E-15 3 -0.388578E-15 -1.00000 2.00000 -1.00000 -0.402456E-15 4 -0.943690E-15 -0.111022E-15 -1.00000 2.00000 -1.00000 5 -0.166533E-15 -0.735523E-15 -0.291434E-15 -1.00000 2.00000 SVSORT_TEST SVSORT sorts a vector D, and the corresponding columns of a matrix V. First row = entries of D. Corresponding columns of V below. 0.307493 0.737357E-01 0.684423 0.270468 0.951468E-01 11.0000 12.0000 13.0000 14.0000 15.0000 21.0000 22.0000 23.0000 24.0000 25.0000 31.0000 32.0000 33.0000 34.0000 35.0000 41.0000 42.0000 43.0000 44.0000 45.0000 51.0000 52.0000 53.0000 54.0000 55.0000 After sorting D and rearranging V: 0.684423 0.307493 0.270468 0.951468E-01 0.737357E-01 13.0000 11.0000 14.0000 15.0000 12.0000 23.0000 21.0000 24.0000 25.0000 22.0000 33.0000 31.0000 34.0000 35.0000 32.0000 43.0000 41.0000 44.0000 45.0000 42.0000 53.0000 51.0000 54.0000 55.0000 52.0000 praxis_test Normal end of execution. 6 October 2025 6:31:05.560 PM